@inproceedings{afc0ee5e749f4842a5e417532651f5de,
title = "Line segment covering of cells in arrangements",
abstract = "Given a collection L of line segments, we consider its arrangement and study the problem of covering all cells with line segments of L. That is, we want to find a minimum-size set L′ of line segments such that every cell in the arrangement has a line from L′ defining its boundary. We show that the problem is NP-hard, even when all segments are axis-aligned. In fact, the problem is still NP-hard when we only need to cover rectangular cells of the arrangement. For the latter problem we also show that it is fixed parameter tractable with respect to the size of the optimal solution. Finally we provide a linear time algorithm for the case where cells of the arrangement are created by recursively subdividing a rectangle using horizontal and vertical cutting segments.",
author = "Matias Korman and Poon, {Sheung Hung} and Marcel Roeloffzen",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.; 9th International Conference on Combinatorial Optimization and Applications, COCOA 2015 ; Conference date: 18-12-2015 Through 20-12-2015",
year = "2015",
doi = "10.1007/978-3-319-26626-8_12",
language = "English",
isbn = "9783319266251",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "152--162",
editor = "Donghyun Kim and Weili Wu and Ding-Zhu Du and Zaixin Lu and Wei Li",
booktitle = "Combinatorial Optimization and Applications - 9th International Conference, COCOA 2015, Proceedings",
address = "Germany",
}